Question

Solve the equation (2^2x)/( 2^x+5) = 1 algebraically using two different initial steps as directed below.

. Write each side as a power of 2

Answer 1

x = 5

Explanation:

Given equation as:

`(2^2x)/(2^(x+5))` = 1

now,

writing each side as power of 2

2⁰ = 1

therefore,

`(2^2x)/(2^(x+5))` = 2⁰

also, we know the property that , when the number having the same bases gets divided , the powers of the number gets subtracted

therefore,

`2^(2x-(x+5))` = 2⁰

now for the equality the power of 2 both sides should be equal

thus,

⇒ 2x-(x+5) = 0

or

⇒ 2x = x + 5

or

⇒ 2x - x = 5

or

⇒ x = 5